# Irreducible Polynomial : Galois Group

4. Find an irreducible polynomial defining the field extension K = Q (cube root 2, sq root − 3) over Q . Is K a normal extension of Q ? What is the Galois group for the splitting field of the polynomial defining K over Q ?

© BrainMass Inc. brainmass.com October 9, 2019, 3:44 pm ad1c9bdddfhttps://brainmass.com/math/linear-transformation/irreducible-polynomial-galois-group-11756

#### Solution Summary

The Galois group for the splitting field of a polynomial is determined.

$2.19